Poincaré Lemma on Quaternion-like Heisenberg Groups
Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 495-508
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For smooth functions ${{a}_{1}}\,,\,{{a}_{2}}\,,\,{{a}_{3}}\,,\,{{a}_{4}}\,$ on a quaternion Heisenberg group, we characterize the existence of solutions of the partial differential operator system ${{X}_{1}}f\,=\,{{a}_{1}},\,{{X}_{2}}f=\,{{a}_{2}},\,{{X}_{3}}f\,=\,{{a}_{3}},\,\text{and}\,{{X}_{4}}f\,=\,{{a}_{4}}$ . In addition, a formula for the solution function $f$ is deduced, assuming solvability of the system.
Mots-clés :
93B05, 49N99, bracket generating property, quaternion Heisenberg group, curl, integrability condition, Poincaré lemma
Chang, Der-Chen; Yang, Nanping; Wu, Hsi-Chun. Poincaré Lemma on Quaternion-like Heisenberg Groups. Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 495-508. doi: 10.4153/CMB-2017-027-4
@article{10_4153_CMB_2017_027_4,
author = {Chang, Der-Chen and Yang, Nanping and Wu, Hsi-Chun},
title = {Poincar\'e {Lemma} on {Quaternion-like} {Heisenberg} {Groups}},
journal = {Canadian mathematical bulletin},
pages = {495--508},
year = {2018},
volume = {61},
number = {3},
doi = {10.4153/CMB-2017-027-4},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-027-4/}
}
TY - JOUR AU - Chang, Der-Chen AU - Yang, Nanping AU - Wu, Hsi-Chun TI - Poincaré Lemma on Quaternion-like Heisenberg Groups JO - Canadian mathematical bulletin PY - 2018 SP - 495 EP - 508 VL - 61 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-027-4/ DO - 10.4153/CMB-2017-027-4 ID - 10_4153_CMB_2017_027_4 ER -
%0 Journal Article %A Chang, Der-Chen %A Yang, Nanping %A Wu, Hsi-Chun %T Poincaré Lemma on Quaternion-like Heisenberg Groups %J Canadian mathematical bulletin %D 2018 %P 495-508 %V 61 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-027-4/ %R 10.4153/CMB-2017-027-4 %F 10_4153_CMB_2017_027_4
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